Sums and substracts in Early Childhood Education
Keywords:
addition, subtraction, arithmetic operations, early childhood education, mathematical educationAbstract
This study examines the process that spans from real and effective addition and deduction actions to constructing the arithmetic operations of adding and taking away in schoolchildren aged 3, 4 and 5. The underlying logical-mathematical model is that of transformations. For these operations to take place this model must be introduced at the same time as quantification, since it is this simultaneity that leads to numerical relationships. Bearing in mind that the inception of addition and subtraction operations in schoolchildren is subject to the actions of adding and taking away that are developed in a process of mental construction of the logical-mathematical models of transformations of discrete quantities, an early childhood classroom action plan is proposed using a systematic treatment of these operations.Downloads
References
Canobi, K., Reeve, R. & Pattison, P. (2003). Patterns of Knowledge in Children's Addition. Developmental Psychology, 39(3), 21-34.
Canobi, K.(2004). Individual Differences in Children's Addition and Subtraction Knowledge.Cognitive Development, 19(1), 81-93.
Carpenter, T. P. & Moser, J.M. (1979). An investigation of de learning of addition and subtraction. Madison: Wisconsi Research and Development Center for Individualizad Schooling.
Carpenter, T. P. Fennema, E. et al (1999). Children’s Mathematics. Cognitively Guided Instrction.Prtsmouth, NH: Heinemann.
Dickson, L., Brown, M. & Gibson. O. (1991). El aprendizaje de las matemáticas. Cerdanyola: Editorial Labor, S.A.
Fernandez, C. (2001). Aprendizajes numéricos en el ámbito familiar. En A. Gervilla, M. Barreales, R. Galante & Martinez, I.(Eds.), Familia y Educación (pp. 339-348). Málaga: HUM 205.
Fernández, C. (2007). ¿Cómo y cuándo abordar la didáctica de las operaciones de suma y resta?. Bordón, 59(1), 63-80.
Ginsburg, H. & Pappas, S. (2004). SES, Ethnic, and Gender Differences in Young Children's Informal Addition and Subtraction: A Clinical Interview Investigation. Journal of Applied Developmental Psychology, 25(2), 171-192
Hughes, M. (1981). Can Pre-School Children Add and Subtract?. Educational Psychology, 1(3), 207-219.
Mccrink, K. & Wynn, K. (2004). Large, number addition and subtraction by 9-month-old infants. Psycological Science, 15, 776-781.
Mialaret, G. (1984). Las Matemáticas cómo se aprenden, cómo se enseñan. Madrid: Aprendizaje Visor.
Naito, M. & Miura, H. (2001). Japanese Children's Numerical Competencies: Age- and Schooling-Related Influences on the Development of Number Concepts and Addition Skills. Developmental Psychology, 37(2), 17-30.
Robinson, K. (2001). The Validity of Verbal Reports in Children's Subtraction. Journal of Educational Psychology.93 (1), 211-222.
Starkey, P. & Gelman, R. (1982). The development of addition and subtraction abilities prior to formal schooling in arithmetic. En T. Carpenter, J. Moser & T. Romberg (Eds). Addition and subtraction: A cognitive perspective. (pp. 99-116). Hillsdale, Nueva Jersey: Lawrence Erlbaum Associates.
Vergnaud, G. (1985). L'enfant, la mathématique et la réalité. New York: Peter Lang.
Vilette, B. (2002). Do young children grasp the inverse relationship between addition and subtraction? Evidence against early arithmetic. Cognitive Development, 17, 1365-1383.
Zur, O. & Gelman, R. (2004). Young Children Can Add and Subtract by Predicting and Checking. Early Childhood Research Quarterly, 19(1),121-137.